Prove of the complicated integral

  • #1
Hi experts!

How to prove this integral?

[itex]\frac{2}{e^{5}}[/itex][itex]\leq[/itex][itex]\int[/itex][itex]\int_{D}[/itex]e[itex]^{-(x^{2}+y^{2})}[/itex]dxdy[itex]\leq[/itex]2
on
D=[0,1] and [0,2]

Here D is subscript of the 2nd integral.

I seriously have no idea how to start. I am 100% blank with this question.

Thanks in advance.
 

Answers and Replies

  • #2
22,089
3,286
What is the maximum/minimum value that [itex]e^{-(x^2+y^2)}[/itex] can attain??
 
  • #3
726
1
Why not just calculate the integral? The rectangle (0,1) x (0,2) is diffeomorphic to a circle (or the circle minus a set of measure zero) so use the change of variables theorem.
 

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